ARTICLE IN PRESS
Deep-Sea Research II 53 (2006) 2632–2655 www.elsevier.com/locate/dsr2
Biological control of the vernal population increase of Calanus finmarchicus on Georges Bank
Xingwen Lia, Dennis J. McGillicuddy Jr.a,Ã, Edward G. Durbinb, Peter H. Wiebea
aWoods Hole Oceanographic Institution, Woods Hole, MA 02543, USA bGraduate School of Oceanography, University of Rhode Island, South Ferry Road, Narragansett, RI 02282, USA
Accepted 25 August 2006 Available online 9 November 2006
Abstract
An adjoint data assimilation approach was used to quantify the physical and biological controls on Calanus finmarchicus N3–C6 stages on Georges Bank and its nearby environs. The mean seasonal cycle of vertically averaged distributions, from 5 years of the GLOBEC Georges Bank Broad-Scale Surveys between January and June, was assimilated into a physical–biological model based on the climatological circulation. Large seasonal and spatial variability is present in the inferred supply sources, mortality rates, computed molting fluxes, and physical transports. Estimated mortalities fall within the range of observed rates, and exhibit stage structure that is consistent with earlier findings. Inferred off-bank initial conditions indicate that the deep basins in the Gulf of Maine are source regions of early stage nauplii and late-stage copepodids in January. However, the population increase on Georges Bank from January to April is controlled mostly by local biological processes. Magnitudes of the physical transport terms are nearly as large as the mortality and molting fluxes, but their bank-wide averages are small in comparison to the biological terms. The hypothesis of local biological control is tested in a sensitivity experiment in which upstream sources are set to zero. In that solution, the lack of upstream sources is compensated by a decrease in mortality that is much smaller than the uncertainty in observational estimates. r 2006 Elsevier Ltd. All rights reserved.
Keywords: Calanus finmarchicus; Population dynamics; Georges Bank; Inverse modeling; Adjoint method
1. Introduction including hatching from eggs, development through six naupliar stages (N1–N6) and five copepodid Calanus finmarchicus is a key zooplankton species stages (C1–C5), non-obligatory diapause, and ma- in the Georges Bank (GB)/Gulf of Maine (GOM) turation to adulthood (C6). Large seasonal varia- ecosystem, and is an important food source for bility is present in the annual cycle of the C. larval stages of commercially important fish species. finmarchicus population on GB (e.g., Davis, 1987). Its life history is multifaceted (Carlotti, 1996), This species dominates the zooplankton biomass on the bank in spring/early summer, but is almost absent from the crest of the bank from fall to the ÃCorresponding author. Tel.: +1 508 289 2683; fax: +1 508 457 2194. start of winter. Models have been used to elucidate E-mail address: [email protected] aspects of the population dynamics of C. finmarch- (D.J. McGillicuddy Jr.). icus (Lynch et al., 1998; Miller et al., 1998; Tittensor
0967-0645/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.dsr2.2006.08.011 ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2633 et al., 2003; Zakardjian et al., 2003; Speirs et al., by counter-clockwise flow along the perimeter of the 2005; Johnson et al., 2006), but the processes basin, cyclonic gyres over the deep basins, clockwise controlling the annual population cycle remain circulation around GB, inflow through the North- enigmatic. In particular, the relative roles of east Channel, and outflow via the western edge of recruitment, development, mortality, and physical the southern flank (Beardsley et al., 1997). transport have yet to be quantified in a systematic Observations from the Global Ocean Ecosystem and spatio-temporally explicit manner. Such knowl- Dynamics (GLOBEC) GB broad-scale surveys (Fig. edge is not only important to evaluate the role of C. 1) provide an opportunity to investigate the physical finmarchicus in the food web, but also to predict the and biological mechanisms controlling the popula- consequences of climatic change on this organism tion dynamics of C. finmarchicus. Our approach is (Hirche, 1996). to compute a monthly stage-based climatology from Abundance and distribution patterns of C. these observations, and to assimilate these data into finmarchicus populations in the region are strongly a physical–biological model based on the climato- influenced by physical mechanisms. The physical logical hydrodynamics of the region (Lynch et al., environment is complex (e.g., Bigelow, 1927; Flagg, 1996). The inverse problem (schematized in Fig. 2) 1987; Butman et al., 1987; Lynch et al., 1996; is formulated by specification of the velocity Gangopadhyay et al., 2003). North of GB is the and diffusivity fields, observed monthly distribu- GOM, comprising three deep basins: Jordan Basin, tions on GB, and development rates that depend on Wilkinson Basin, and Georges Basin. South of GB temperature and the availability of food (Campbell is the continental slope and the Slope Water. To the et al., 2001). The adjoint method is used to infer west, GB is separated from Nantucket Shoals by the stage-based mortality fields, off-bank initial condi- Great South Channel; to the northeast, it is tions, and sources of the youngest stage resolved by separated from the Scotian Shelf by the Northeast the model (N3). Solutions resulting from the Channel. The bank itself consists of distinctive inversion procedure are then diagnosed to quantify subregions, such as the northern flank, the northeast physical and biological controls on the climatologi- peak, the southern flank, and the crest (Fig. 1). The cal abundance and distribution of C. finmarchicus mean circulation in the GOM/GB area is dominated on GB.
Fig. 1. Station locations of the US GLOBEC GB broad-scale surveys between 1995 and 1999. MOCNESS samples are available at stations denoted by the black dots, and pump samples are available at stations denoted by circles. ARTICLE IN PRESS 2634 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655
Abundances of C4,C5 and C6 were higher than those of C2 and C3, implying that the majority of the animals in these later stages belonged to a prior generation. C5 and C6 abundances were relatively high near the northern flank. In February, abundances of all stages except for C5 increased. The population structure was similar to January, in that relative abundance system- atically decreased with stage between N3 and C4. Stage N3 was abundant all across the bank. High abundance centers of N4–N6 were located in the northwest portion and on the northeast peak. The maximum abundances of C1–C3 were slightly south of the northeast peak. Moderate numbers of C6 were located along the northern flank and the eastern portion of the bank. In March, nauplii became more numerous all across the bank. Numbers of copepodids and adults Fig. 2. Schematic diagram of the forward model (top), list of the increased, and the southern flank became a popula- specified and inferred model inputs (middle), and space/time tion center of copepodids, particularly the earlier characteristics of the various components used in the inverse problem described herein (bottom). stages C1–C3. Older stages tended to be more abundant around the bank periphery and less so on the crest. 2. Methods Abundances of copepodids continued increasing in April, whereas naupliar abundance remained 2.1. Observations relatively constant. The resulting springtime age structure of N3–C5 was much more even than in the C. finmarchicus observations were derived from winter months. The April distribution of N3–C5 on samples collected by plankton pumps (Durbin et al., the bank was nearly uniform, although for most 2000a) for N3–C1 and the Multiple Opening and stages the crest contained slightly lower abundance Closing Net and Environmental Sensing System than the surrounding areas. For the adult stage, the (MOCNESS, Wiebe et al., 1985) for C2–C6 during contrast in abundance between the crest and bank GLOBEC GB broad-scale surveys from January to periphery remained more pronounced. June between 1996 and 1999, and from February to In May, abundances of N3–C3 declined, especially June in 1995 (Durbin et al., 2000b). Monthly on the crest. In contrast, the abundances of C4 and climatological values for each station (Fig. 1) were C5 increased slightly from April to May, maintain- obtained by averaging the observations over the 5- ing their relatively uniform distribution over the year period. Climatological values were then objec- bank. The overall abundance of adults remained tively analyzed (Hendry and He, 2002) to construct nearly constant, with a decrease in abundance on spatial maps. the crest compensated by modest increases along the Monthly climatological distributions for each C. bank periphery. finmarchicus stage (Fig. 3) form the basic dataset for In June, abundances of nauplii increased again, the inverse modeling. In January, a substantial indicating the initiation of a new generation. number of nauplii were present on the bank. The Abundances of copepodids dropped sharply on age composition (Fig. 4A) showed numbers of the bank, with particularly low abundances of N34N44N54N64C14C24C3, indicating the on- C1–C6 on the crest. Along the bank periphery, set of reproduction. Relatively high abundances of C4–C6 remained relatively numerous. N3 and N4 appeared in the north portion of the bank, with the maximum abundance center of N5 2.2. Forward model shifted toward the northeast peak. Abundances of C1–C3 were very low on the bank; nauplii had not The forward model is an off-line version (‘‘Aca- developed into these stages on the bank in January. dia’’) of a finite element hydrodynamic model ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2635
Jan Feb Mar Apr May Jun
4.5 3 N
4 4 N
5 3.5 N 6
N 3 1
C 2.5 2 C 2 3 C 1.5 4 C 1 5 C
0.5 6 C
0
2 Fig. 3. Mean monthly distributions of vertically integrated Calanus finmarchicus N3–C6 [log10(1+#/m )] observed between 1995 and 1999. Station locations are indicated by black dots, which consists of pump samples for N3–C1 (open circles in Fig. 1) and MOCNESS samples for C2–C6 (black dots in Fig. 1). Geographic coverage of the maps is confined to the area in which the expected error computed in the objective analysis is less than approximately 40 percent. Isobaths shown are 60, 100, and 200 m. developed at the Dartmouth Numerical Methods transport calculations. These simulations were run Laboratory (Lynch et al., 1996). The circulation from January 15 to June 15, with observations of C. model includes tidal forcing, wind, and density- finmarchicus specified on a monthly basis (see driven flows (Naimie et al., 1994). The domain of Section 2.3 below). The temporal resolution of the computation includes GB, the GOM, and Scotian hydrodynamic climatology used to drive the trans- Shelf. Horizontal grid spacing is as fine as 1 km in port model is thus coarser than that of the C. regions of steep topography. Archived bimonthly finmarchicus climatology. However, the bimonthly climatologies1 for January–February, March–April, hydrodynamic climatology is demonstrably consis- and May–June were used as input for off-line tent with available observations (Naimie, 1996; Naimie et al., 2001) and represents basic features 1See http://www-nml.dartmouth.edu/ of the circulation system in the domain. ARTICLE IN PRESS 2636 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655
5 (A) Molting fluxes at stages N3–C5 are computed N according to 4.5 3 4 N4 C F ¼ i , (2) N i 3.5 5 Di
3 N6 where the stage-specific duration Di depends on 2.5 C1 both temperature and food availability. In a food
2 C2 abundant condition, the temperature-limited stage 1.5 C duration DT is described by the Belehradek equa- 3 tion 1 C4 Jan Feb Mar Apr May Jun b C5 ðDT Þi ¼ aiðT m aÞ . (3) 5 (B) C6 The parameters ai, a, and b are specified 4.5 Total according to Campbell et al. (2001); Tm is the 4 vertically averaged bimonthly climatological tem- 3.5 perature from Lynch et al. (1996). 3 The effect of food availability on the stage duration was estimated from the Ivlev function 2.5 (e.g., Campbell et al., 2001). At T ¼ 8 1C, the food 2 dependent stage duration DChl is represented as 1.5 1 1 ð Þ ¼ DChl i ð 0:0253 ðChl þ4:968ÞÞ (4) Jan Feb Mar Apr May Jun bið1 e C Þ Fig. 4. Observed (A) and simulated (B) bank-wide averages of 2 with ChlC the food concentration given in terms of stage-specific abundance. Units log10(1+#/m ). 1 carbon (mgCl ). Values of bi were provided by Campbell (2003, personal communication), based The forward model is written on the data presented in Campbell et al. (2001). The food concentration was obtained from the climato- qCi 1 þ v rCi r ðHKrCiÞ logical chlorophyll fields derived from the MAR- qt H MAP observations during 1977–1987 (O’Reilly and ¼ di 1R F i þðF i 1 þ miCiÞð1 di 1Þ. ð1Þ Zetlin, 1996). Although, the chlorophyll climatology is not contemporaneous with the C. finmarchicus Here C is the vertically averaged zooplankton climatology computed herein, we are not aware of concentration, H the bottom depth, v the vertically any other regional climatology of in situ chlorophyll averaged velocity and K the horizontal diffusivity data that would be more suitable for the present from the bimonthly climatology. Prior to assimila- application. The ratio of carbon to chlorophyll was tion, the vertically integrated abundance data set to 50 mg C (mg Chl a) 1, consistent with (Fig. 3) were transformed into vertically averaged previous studies (e.g., Hind et al., 2000; Hirche concentrations by dividing by the bottom depth. and Kwasniewski, 1997). The modeled zooplankton concentrations were If we assume that food concentration has the changed back to the vertically integrated abun- same proportionate effect at all temperatures, the dances for presentation, so as to be consistent with temperature and food dependent duration Di is thus the data units of the observations. Subscript i is the stage index, with 1–10 representing N –C , respec- ðD Þ 3 6 D ¼ðD Þ j Chl i . (5) tively. R includes the input sources and mortality of i T i T¼Tm ðDT ÞijT¼8 N3,withdi 1 a function that is 1 at i ¼ 1 and zero at other stages. Fi and mi represent stage-specific We regard the estimation of the stage duration molting flux and mortality, respectively. Sign described above as a first-order approximation of conventions are such that molting flux is positive true food–temperature dependency, ignoring com- and mortality is negative (Eq. (1)). plex details about food–temperature interaction. ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2637
2.3. Inversion procedure where Cm and Cobs are modeled and observed C. finmarchicus concentrations, Nmon the number of The inverse problem is formulated as an optimiza- months in the integration period, Nstage the number tion problem, in which a cost function measuring the of modeled stages, and Nobs the number of model-data misfit is minimized, while being con- observations at each stage in each month. In this strained by the model dynamics (Tziperman and application, we have chosen to assimilate the Thacker, 1989). The adjoint technique can efficiently objectively analyzed maps of C. finmarchicus compute the gradient of the cost function with respect (Fig. 3) rather than the raw observations them- to model parameters and other inputs by integrating selves. This allows us to specify an ‘‘observation’’ at the dynamic model forward and its adjoint model every node on the bank, so Nobs becomes the backward (Li and Wunsch, 2004) in time. A gradient- number of nodes (3688) in the colored areas of Fig. based algorithm is then used to find the minimum of 3. This approach imposes a spatial regularization on the cost function in an iterative procedure. the inversion, set by the correlation length scales The adjoint method is well documented in specified in the objective analysis. literature (Wunsch, 1996). This method has been The cost function is minimized in an iterative widely applied to optimal control problems in procedure consisting of the following steps: (1) engineering (Hasdorff, 1976). In meteorology and starting with initial estimate of the control para- oceanography, the use of adjoint techniques can be meters (the unknowns in the C. finmarchicus dated back to the 1980s, for both sensitivity analysis population dynamics model), the forward model is (Hall, 1986) and data assimilation (Thacker and integrated to evaluate the cost function; (2) the Long, 1988). The innovation of the Adjoint Model adjoint model is integrated backward in time to Compiler,2 which produces the adjoint model in a compute the gradient of the cost function with semi-automatic way, helps overcome the burden of respect to the control parameters; and (3) improved writing the adjoint code (Giering and Kaminski, estimates of the control parameters are computed. 1998). The adjoint method has been successfully The control parameters for this problem are applied in ocean state estimation (Moore, 1991; the monthly varying source/sink R (input source+ Stammer et al., 2002) and the study of transient mortality) of N3, mortality mi at stages N4– C6 over tracers (Li and Wunsch, 2003). Lawson et al. (1995, the whole model domain, and the initial off-bank 1996) used this method in simple ecosystem models fields on January 15 where observations were not for biological parameter estimation; also see Hof- present (model domain is larger than the area mann and Friedrichs (2001). This method also has plotted in Fig. 3). All control variables were allowed been applied in the GB/GOM region to investigate to vary independently at corresponding model the mechanisms controlling the distributions of nodes. The first-guess values of all control variables adult Pseudocalanus spp. (McGillicuddy et al., were set to zero. 1998), and P. moultoni/P. newmani (McGillicuddy Within the iterative framework, the control and Bucklin, 2002). Note that the present formula- parameters are updated with a quasi-Newton tion of the inverse problem for C. finmarchicus algorithm for solving large nonlinear optimization includes more detailed population dynamics (multi- with simple bounds (Byrd et al., 1995; Zhu et al., ple life stages, temperature- and food-dependent 1994). Bound constraints on control variables keep stage duration, density-dependent mortality) than the inferred parameters within meaningful limits. these prior studies of Pseudocalanus. We impose upper bounds of zero for mortality rates We seek to minimize the misfit between simulated (recall mortality is negative given the sign conven- and observed concentrations of C. finmarchicus, tion in Eq. (1)) and lower bounds of zero for initial subject to the constraint that the forward model zooplankton concentrations. In order to speed up (Eq. (1)) is strictly obeyed. The model-data misfit, or convergence, the control variables were precondi- cost function J, is defined to be tioned with u ¼ ui=ai, where ui are the control variables and ai are the corresponding precondi- N NXmon Xstage XNobs tioners. The preconditioning transformation needs 1 1 1 2 J ¼ ðCm CobsÞ , (6) not define variables with any simple physical Nmon Nstage Nobs k j i interpretation, but was used to reduce the con- ditioning number (the ratio of the largest to the 2http://www.autodiff.com/tamc/. smallest eigenvalues) of the Hessian matrix ARTICLE IN PRESS 2638 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655
(e.g., Tziperman and Thacker, 1989). Precondi- abundances of C1–C4 on the entire bank, and tioners were 20, 5.6, 2.1, 0.8, 0.1, 0.2, 0.3, 1, 7, 6 (# moderate abundances of C5 and C6 along the 3 m ) for the initial concentrations of N3–C6 in the bank’s northern periphery. In February, naupliar GOM, respectively. The values of preconditioners and younger copepodid stages increased dramati- approximated the mean concentrations of C. cally, whereas C5 and C6 showed modest decreases finmarchicus observed in the southern GOM in and increases, respectively. During March–April, January broad-scale surveys. Concentrations in the the population of C. finmarchicus reached its peak northern GOM (not observed in the broad-scale abundance. In May, abundances of N3–C3 declined, surveys) can be quite different (Durbin et al., 2003). while abundances of C4–C6 continued increasing. However, we lack sufficient data to incorporate Naupliar and C1 abundances increased again in spatial varying preconditioners over the entire June, while C2–C6 decreased, especially on the crest. GOM. In the Slope Water, preconditioners were set to 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 3.2. Inferred initial conditions 3 0.1, 0.1 (# m ) for N3–C6, respectively. These values reflect the low abundance of C. finmarchicus The inversion successfully produced initial con- in slope waters during January (Miller et al., 1991). ditions in the off-bank regions in January (Fig. 6). Moreover, we force concentrations in slope water to Low concentrations of all stages are present in the zero in the forward model, based on the fact that the slope water, as the preconditioners express prior organism generally resides in strata that are too knowledge of the animal’s low abundance in that deep (ca. 500 m) to be readily transported on-bank area during January. In contrast, information from (Miller et al., 1991). This forcing in slope waters is the observations on GB propagated upstream into applied by the addition of an extra term on the the GOM, with moderate abundances of C4,C5 and right-hand side of Eq. (1), independent from the C6 inferred over the deep basins of the Gulf. These estimated mortality. Preconditioners were 10 5 (# results are generally in agreement with the 3 1 7 1 m s ) for R and 10 s for all mortality rates mi 1977–1987 regional climatology for C3–C6 described in the first few iterations, and 10 3 (# m 3 s 1) for R by Meise and O’Reilly (1996). Significant abun- 5 1 and 10 s for mi afterward. Resetting precondi- dance of early naupliar stages (especially N3) is also tioners of R and mi reflects a strategy to recover the inferred. Observations in the southern GOM initial conditions first, followed by the rate para- reported by Durbin et al. (1997) are consistent with meters. Iteration was terminated when the cost these findings; however, there is a paucity of data to function no longer dropped significantly, even by constrain early season abundance of younger stages resetting the preconditioners. in the northern GOM. Nevertheless, the inferred initial conditions suggest emergence from diapause 3. Results and the start of reproduction prior to January, a conclusion made also by Durbin et al. (1997). 3.1. Constrained model performance 3.3. Inferred source/sink of N3 Model performance was dramatically improved by the optimal estimates of initial fields in January, Because N3 is the youngest stage resolved in the space–time varying sources/sinks of N3 and mortal- model, its sources and sinks are aggregated into a ity rates at stages N4–C6. After the inversion, single term (di 1R in Eq. (1)). Positive values model-data misfit was reduced by about 93%, constitute net addition of animals, whereas negative approximately an order of magnitude less than that values constitute net removal. The source of N3 is resulting from the initial values of the control the unknown molting from the unresolved stage N2, variables (all zero). The inversion successfully whereas sinks of N3 include both molting to N4 reproduced the most salient features of the observa- (computed from the N3 distribution and Eq. (2) tions both in terms of bank-wide averages (Fig. 4B) above) and the unknown mortality. Physical trans- and spatial distributions (Fig. 5). The initial model port terms can act as both sources and sinks, conditions on GB were identical to the observa- depending on the spatial gradients of the organism tions, with relatively high abundances of N3 and N4 and the specified velocity and diffusivity fields. The in the northern portion of the bank, relatively high di 1R term thus amalgamates an inferred source abundance of N5 on the northeast peak, low (molting from N2) and sink (mortality of N3)to ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2639
Jan Feb Mar Apr May Jun 4.5 3 N
4 4 N
3.5 5 N
3 6 N
1 2.5 C 2
C 2 3 C 1.5 4 C 1 5 C
0.5 6 C
0
2 Fig. 5. Modeled abundances of C. finmarchicus [vertically integrated, presented in units of log10(1+#/m )] after data assimilation, with the same mapping area as Fig. 3. Isobaths are 60, 100, and 200 m.
achieve a solution that is consistent with observed although a net source is evident all along the distributions of N3 and the sources and sinks that northern edge of the bank. Positive values persist on are specified in the forward model (transport and the northeast peak and along the northern edge molting to N4). through March–April. Mortality is prevalent on the The sign of the inferred di 1R term is generally southern flank inshore of the 200 m isobath from positive, owing to its predominate role as a source January–February to February–March. Net sources of N3 copepodids (Fig. 7). In January–February, the and sinks are weak throughout in April–May, and strongest positive values appear on the northeast then become strong again along the bank periphery peak and the northwest portion of the bank, in May–June. Note that a strong source persists in ARTICLE IN PRESS 2640 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655
4 N N N N C 3 4 5 6 1 3 2 1 0
C2 C3 C4 C5 C1
2 Fig. 6. Optimal initial fields for C. finmarchicus stages N3–C6 [vertically integrated, presented in units of log10 (1+#/m )]. The first estimates of initial values outside the data area (white area in Fig. 3) are zeros. Isobaths are 60 and 200 m.
Jan–Feb Feb–Mar Mar–Apr Apr–May May–Jun 3 N
–0.05 0 0.05 –0.2 0 0.2 –0.2 0 0.2 –0.2 0 0.2 –0.2 0 0.2
2 1 Fig. 7. Inferred net sources/sinks of N3 (vertically integrated, presented in units of # m s ). Isobaths are 60 and 200 m. the Northeast Channel throughout the simulation in next. Strong seasonal variability in molting flux is order to maintain the high abundances of N3 evident amongst the various stages (Fig. 8). During observed there. January–February, the nauplii developed mostly on Another salient feature of the inferred di 1R GB (except on the southwestern portion) and the distribution is the presence of bands of alternating Great South Channel. Development of copepodids small-scale sources and sinks. These tend to occur on the bank was modest, owing to their low mostly along pathways of high transport (e.g., the abundance during that period. During February– northern and southern flanks), where the advection March, molting fluxes of nauplii were strong on GB terms are of the same order as the biological terms and its adjacent off-bank regions; in the deep basins (see below). In these areas, we tend to interpret the of the GOM, molting fluxes of the youngest spatial average of di 1R (which is near zero along naupliar stages were most prominent. Molting the transport pathway) rather than its detailed fluxes of both nauplii and younger stage copepodids spatial distribution, as these structures may be increased substantially during March–April, with sensitive to mesh resolution. There is an additional the overall amplitude decreasing with stage in factor to consider pertaining to the strong sources accordance with the age structure of the population. and sinks at the offshore periphery of the southern Molting fluxes in the GOM were highest in the flank. They occur along the interface between on- youngest naupliar stages, and systematically de- bank areas constrained by the GLOBEC data and creased with stage. In April–May, naupliar molting the slope waters south of the bank in which the fluxes increased in the GOM, but decreased on GB. copepod concentrations are forced to zero. These In contrast, copepodid molting fluxes increased in features are likely to be an artifact of the forcing both the GOM and GB. During May–June, molting applied to the slope waterside of that boundary, and fluxes of stages N3–N5 remained large on the bank, therefore we are not inclined to interpret results of while those of N6–C4 dropped sharply. Molting the inversion in that area. fluxes in the GOM decreased for all stages except for C4 and C5 copepodids, which increased in 3.4. Computed molting fluxes May–June. It is interesting that significant molting fluxes The computed molting fluxes quantify the rate at of copepodids west of the Great South Channel which individuals develop from one stage to the did not appear until March–April in our model. ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2641
Jan–Feb Feb–Mar Mar–Apr Apr–May May–Jun N3 F N4 F N5 F N6 F C1 F C2 F C3 F C4 F C5 F
–0.010 0.01 –0.020 0.02 –0.02 00.02 –0.020 0.02 –0.020 0.02 Molting fluxes (# m-2 S-1)
Fig. 8. Computed monthly mean molting fluxes (vertically integrated, presented in units of # m 2 s 1). Isobaths are 60 and 200 m. ARTICLE IN PRESS 2642 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655
Smith and Lane (1988) found that C. finmarchicus 3.6. Computed divergence of advective fluxes copepodids did not begin to increase in the New York Bight until March. The increase occurred first The influence of advection varied considerably in to the east, suggesting an advective input from time and space, with distinct patterns amongst the upstream, consistent with the present model. various life stages evident in the advective flux divergence4 (Fig. 12). Positive (negative) values 3.5. Inferred mortality indicate an increase (decrease) in abundance by the divergence of the advective fluxes. In Januar- The inferred mortality distributions reveal sig- y–February, the most pronounced signals occurred nificant structure in time and space (Fig. 9). In in the youngest stages, in association with south- general, highest mortalities occurred on the bank westward transport of the abundant nauplii present and in the adjacent areas of the Great South on the NEP. Advection along the southern flank Channel, the Northeast Channel, and southern was illuminated by alternating small-scale regions of Georges Basin. Two major episodes of mortality positive and negative values, which average out to affected the nauplii and early copepodids (C and near zero along the transport pathway. The overall 1 magnitude of the advective terms decreased system- C2), the first at the beginning of the growing season (January–February and February–March) atically with stage in January–February, such that and the second during May–June. Mortality of there are no discernible patterns in the copepodid these stages was relatively modest during the stages. intervening period (March–April and April–May). From February–March into March–April, south- westward transport intensified and reached farther Copepodid stages C3 and C4 suffered comparatively little mortality throughout the simulated time down the southern flank. During this time the period, except for a few hotspots in the southern advective influence also spread into the older stages Great South Channel in April–May, and the eastern as they increase in abundance. Note that during this side of the crest during May–June. Mortality of the time an advective source of nauplii and early stage copepodids appeared west of the Great South oldest stages C5 and C6 was very low at the beginning of the growing season and generally Channel leading into the southern New England increased over time. shelf, confirming that westward transport lies at the Spatial coherence in mortality patterns makes it heart of the apparent consistency of the solution possible to compute meaningful bank-wide3 with the findings of the Smith and Lane (1988) averages (Fig. 10). In January–February, the described above. naupliar and younger copepodid stages bore the In April–May, the magnitude of the advective brunt of the losses: mortality peaked at copepodid terms decreased in the naupliar and first copepodid stages as they temporarily declined in abundance. In C1, and decreased monotonically to the adult stage. In February–March, mortality of the younger contrast, advection of the copepodid stages C2–C5 naupliar stages decreased and oldest copepodid intensified, with the transport pathway beginning to stages began to increase, resulting in a bimodal reach all the way around the bank. The around- stage distribution of mortality. This bimodal bank transport became even more prominent in characteristic persisted in March–April, albeit with May–June, particularly in the younger naupliar lower mortality in the naupliar and early copepodid stages. stages. The bimodality was accentuated in the last two bimonthly periods due to increasing mortality 3.7. Computed divergence of diffusive fluxes in the oldest copepodid stages and the sharply increasing mortality of N5–C2 in May–June. Inter- The divergence of the diffusive fluxes (Fig. 13) estingly, this bimodal characteristic is robust in was dominated by small-scale structures, transport- the spatially and temporally averaged mortality ing these animals down-gradient. The most promi- (Fig. 11). nent organized feature in the fields is a banded
4In this context, the term divergence is used to describe the 3For the purposes of these and all subsequent bank-wide mathematical operator ðq=qxÞþðq=qyÞ. When operating on averages, Georges Bank is defined to be the area inside the 200 m advective or diffusive fluxes, the result can be either positive isobath, bounded by 68.81W meridian to the west. (convergence) or negative (divergence in the more specific sense). ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2643
Jan–Feb Feb–Mar Mar–Apr Apr–May May–Jun 4 N 5 N 6 N 1 C 2 C 3 C 4 C 5 C 6 C
–0.20 0.2 –0.20 0.2 –0.2 00.2 –0.20 0.2 –0.20 0.2 Mortality Rates (d-1)
Fig. 9. The spatial distribution of the inferred mortality rates (d 1). Plot area is zoomed in on Georges Bank to show detail in that region. Mortality estimates are negligible in the off-bank areas in which concentrations are not constrained by observations. Isobaths are 60 and 200 m. structure along the southern flank of GB comprised dance of C. finmarchicus on the bank and its of strips of negative and positive values at the edge absence in the adjacent slope waters.5 In general, of the shelf break. These are associated with a net off-bank diffusive transport operating on the con- 5Recall that the model solution is forced to zero concentration centration gradient maintained by the high abun- in slope waters south of GB. ARTICLE IN PRESS 2644 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655
Spatial averaged mortality rate (d –1) on GB 0
–0.1 JF
–0.2 0
–0.1 FM
–0.2 0
–0.1 MA
–0.2 0
–0.1 AM
–0.2 0
–0.1 MJ
–0.2 N4 N5 N6 C1 C2 C3 C4 C5 C6
Fig. 10. Time series of mortality rates (d 1) spatially averaged on GB.
Spatial averaged mortality rate (d –1) on GB provide insight into their relative effect on C. 0 finmarchicus population dynamics (Fig. 14). On –0.02 average, biological reaction terms govern the annual population cycle on GB. The space- –0.04 time averaged convergences of advective and –0.06 diffusive fluxes over GB are small relative to net molting fluxes (Fi 1 Fi) and mortality. The –0.08 standard deviations of physical transports, however, –0.1 are large and vary with stage and time. Casting
–0.12 the term balances in terms of magnitude (Fig. 15), N4 N5 N6 C1 C2 C3 C4 C5 C6 physical transports are clearly of the same order as the biological sources and sinks. Thus, Fig. 11. Temporal mean (January–June) of spatially averaged physical transports are locally important, mortality rates (d 1) on GB. even though inputs and outputs tend to counter- the net effect of diffusion in the interior of GB and balance each other when spatially averaged over the in the GOM is rather modest, tending to smooth out bank. peaks in the distribution of the organism. Although their net effect is small, the bank-wide averages of the transport terms do exhibit some clear trends. For example, diffusive transport off the 3.8. Bank-wide term averages bank constitutes a net loss of C. finmarchicus for all stages at all times. The term maps (Fig. 13) suggest The temporally and spatially averaged values of this results primarily from diffusive flux across the those physical and biological controls on GB shelf break on the southern flank (see above). ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2645
Jan–Feb Feb–Mar Mar–Apr Apr–May May–Jun
0.05 3
N 0
–0.05
0.02 4
N 0 –0.02
0.01 5
N 0 –0.01
0.01 6
N 0 –0.01
x 10–3
1 5 C 0 –5
x 10–3
2 5 C 0 –5
x 10–3
3 5 C 0 –5
x 10–3
4 5 C 0 –5
x 10–3
5 5 C 0 –5
x 10–3
6 5 C 0 –5
Fig. 12. Computed convergence of the monthly mean advective fluxes (vertically integrated, presented in units of # m 2 s 1). Isobaths are 60 and 200 m.
Generally speaking, advection provides a be a net sink for the older copepodids, espe- net source of naupliar stages N4 and N5 early in cially in April–May and May–June. This the growing season. In contrast, advection tends to latter effect tends to be associated with ARTICLE IN PRESS 2646 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655
Jan–Feb Feb–Mar Mar–Apr Apr–May May–Jun
0.05 3 N 0 –0.05
0.01 4
N 0 –0.01
x 10–3 5 5
N 0 –5
x 10–3 5 6
N 0 –5
x 10–3 5 1 C 0 –5
x 10–3 5 2 C 0 –5
x 10–3 5 3
C 0 –5
x 10–3 5 4 C 0 –5
x 10–3 5 5
C 0 –5
x 10–3 5 6
C 0 –5
Fig. 13. Computed convergence of the monthly mean diffusive fluxes (vertically integrated, presented in units of # m 2 s 1). Isobaths are 60 and 200 m. westward transport off the bank from the The population increase of nauplii and copepodids southern flank into the Great South Channel on GB from January–February through March– (Fig. 12). April results mainly from biological processes. ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2647
N4 N5 N6
1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 0 0 0 MJ MJ MJ AM AM AM Mor Mol MA Mor Mol MA Mor Mol MA FM Ten FM Ten FM Ten JF Adv Dif JF Adv Dif JF Adv Dif
C1 C2 C3
1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 0 0 0 MJ MJ MJ AM AM AM Mor Mol MA Mor Mol MA Mor Mol MA FM Ten FM Ten FM Ten JF Adv Dif JF Adv Dif JF Adv Dif
C4 C5 C6
1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 0 0 0 MJ MJ MJ AM Mol AM AM Mol MA Mor MA Mor Mol MA Mor FM Dif Ten FM Ten FM Dif Ten JF Adv JF Adv Dif JF Adv
Fig. 14. Temporally and spatially averaged term balances on GB. Here Adv(ection) ¼ r ðvCiÞ; Dif(fusion) ¼r ðHKrCiÞ=H; Ten(dency) ¼ qCi=qt; Mor(tality) ¼ miCi; Mol(ting flux, net) ¼ Fi 1–Fi, i ¼ 2, 3,y,10. Values are presented on a log scale with units of 3 1 log10(1+# m d ). Blue bars represent negative values, red bars represent positive values. Gray bars represent standard deviations.
N4 N5 N6
1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 0 0 0 MJ MJ MJ AM Mol AM Mol AM Mol MA Mor MA Mor Mor FM Ten FM Ten MA FM Ten JF Adv Dif JF Adv Dif JF Adv Dif C1 C2 C3
1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 0 0 0 MJ MJ MJ AM Mol AM Mol AM Mol Mor MA Mor MA Mor MA FM Ten FM Ten FM Ten JF Adv Dif JF Adv Dif JF Adv Dif C4 C5 C6
1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 0 0 0 MJ MJ MJ AM Mol AM Mol AM Mol Mor MA Mor MA Mor MA FM Ten FM Ten FM Ten JF Adv Dif JF Adv Dif JF Adv Dif
Fig. 15. Temporally and spatially averaged term magnitudes on GB. Here Adv(vection) ¼r ðvCiÞ; Dif(fusion) ¼r ðHKrCiÞ=H; Ten(dency) ¼ qCi=qt; Mor(tality) ¼ miCi; Mol(ting flux, net) ¼ Fi 1–Fi, i ¼ 2, 3,y,10. Values are presented on a log scale with units of 3 1 log10(1+# m d ). Term magnitudes are shown as blue bars; gray bars represent standard deviations.
For each life stage, the input molting flux (Fi 1)is leaving it. However, mortality strongly limits the rate greater than the output molting flux (Fi). More of population increase. The net change in abundance animals are entering into the population than are thus results from a relatively modest difference ARTICLE IN PRESS 2648 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 between net molting fluxes and mortalities of port in controlling temporal changes in abundance comparable magnitude. (Fig. 14). The April–May period is characterized by a In order to quantify the impact of the upstream significant decrease in naupliar abundance. These sources, an additional inversion was undertaken in results suggest this decline is primarily controlled by which all off-bank sources were eliminated. Speci- a decrease in net molting flux rather than an fically, all off-bank concentrations were set to zero increase in mortality. Indeed, naupliar mortality in the initial condition, and the off-bank sources of actually tends to decrease during this period. N3 (R in Eq. (1)) were assumed to be null Interestingly, the N4 and N5 net molting fluxes throughout the duration of the simulation. The become negative in April–May, indicating that resulting abundance fields (not shown) are quite input of new recruits is not sufficient to keep up similar to the baseline case (Fig. 5), although the fit with the maturation rate of these stages. That trend to the observations (as reflected in the final value of reverses in May–June, with N4 and N5 net molting the cost function) is not quite as good as the fluxes regaining positive values. solution in which the off-bank sources are active. The May–June rebound of the naupliar stages are How was the inverse model able to match the not mimicked in the copepodid stages, which all observations in the absence of upstream sources? tend to decrease during that period. For adults, the One way is to increase the inferred local source of decline is brought about by an increase in mortality N3 on GB. Indeed, the inversion procedure did that outpaces an increase in net molting flux. In increase the net source of N3 (di 1R in Eq. (1); see contrast, the decline of C5 occurs in association with Fig. 7 for maps from the baseline inversion) by an a decrease in net molting flux and mortality that is average of 33% on the bank during the period from only slightly lower than its value from the prior January to June. The other way to counterbalance period. The most precipitous decline in copepodids elimination of advective transport of C. finmarchi- occurs in the younger stages, with C3 and C4 cus to GB in the second model is to decrease the experiencing negative net molting fluxes during this inferred mortality rates (Fig. 16). Surprisingly, the period. Net molting fluxes of C1 and C2 remain reduction in mortality required to compensate for positive, so the late season decline in their abun- the lack of upstream sources is indistinguishably dance is brought about primarily by mortality in small given the range of experimental determina- excess of net molting flux. tions of mortality (see Section 4.2 below). That the sources of N3 and mortality fields 4. Discussion inferred in the two cases are so similar indicates upstream sources do not control the springtime 4.1. Is the vernal population increase under biological population increase (Fig. 16). If upstream sources control? were critical, then fitting the data with the second
What controls the springtime profusion of C. finmarchicus on GB? The results presented herein Spatial averaged mortality rate (d –1) on GB 0 are suggestive of two mechanisms. First, the inverse procedure generated off-bank initial conditions that –0.02 contained significant numbers of both nauplii and –0.04 copepodid stages in the deep basins of the GOM upstream of GB (Fig. 6). The inferred initial –0.06 conditions are consistent with available observa- –0.08 tions of the later stage copepodids (Meise and O’Reilly, 1996), and indicate that advective supply –0.1 black: baseline inversion contributes to the vernal population increase on –0.12 gray: no upsteam sources GB. Indeed, earlier modeling studies have focused on the importance of this pathway (Lynch et al., N4 N5 N6 C1 C2 C3 C4 C5 C6 1998; Miller et al., 1998; Hannah et al., 1998). Fig. 16. Temporal mean (January-June) of spatially averaged Despite this apparent advective connection, bank- mortality rates (d 1) on GB for the baseline solution (black bars wide average term balances indicate the predomi- as in Fig. 11) and the solution in which all upstream sources were nance of biological processes over physical trans- set to zero (gray bars; see text). ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2649
voracious planktonic hydroids has been estimated to result in removal of 50–100% of the daily production of young copepods (Madin et al., 1996). The general pattern of the inferred stage-specified mortality (Fig. 11) is similar to estimates derived from a vertical life table analysis of the same data by Ohman et al. (2002). Both studies suggest relative maxima in mortality in the late naupliar/early copepodid stages and the later copepodid stages.7 However, the mortalities estimated herein are systematically lower than those reported by Ohman et al. by approximately 20–40%. There are several possible reasons for these Fig. 17. Cartoon schematic comparing the results of the baseline differences. To begin with, the vertical life table inversion with a sensitivity experiment in which all upstream approach is not spatially explicit and therefore sources of C. finmarchicus were set to zero. cannot account directly for the effects of advection (Aksnes and Ohman, 1996; Aksnes et al., 1997). model would have required a large increase (on the However, advection is an unlikely explanation for order of 100% or more) in the local source of N3 on the differences in the mortality estimates for two GB, and/or unrealistically low values of mortality. reasons. First, analysis of the present model Alternatively, the second model might not have solution indicates the net impact of advection is been able to fit the data at all. The fact that the small relative to molting and mortality terms in the second model can match the observations with only population dynamics equation. Second, results modest adjustments to the two control parameters presented in the preceding section illustrate how therefore suggests a secondary role for upstream elimination of upstream sources can be compen- sources during this time period (Fig. 17). sated by a systematic decrease in mortality esti- It is important to note that this result does not mated by the inversion procedure. By analogy we completely refute the relevance of upstream sources speculate that the inclusion of upstream sources in to the springtime population increase. These calcu- the vertical life table approach would tend to lations are based on initial conditions for GB in increase the resulting mortality estimates, not January that were undoubtedly influenced to some decrease them. degree by upstream sources. However, it is not Another difference between the present study and possible to quantify the impact of upstream sources Ohman et al. (2002) is the temperature used to on the initial conditions. What is clear from these calculate stage duration in the Belehradek function experiments is that upstream sources need not be (Eq. (3)). Our model uses the vertically averaged invoked to simulate the observed population climatological temperature for each node, whereas increase from January to June. Ohman et al. (2002) used the observed temperature at the mean depth occupied by each developmental 4.2. Mortality estimates stage at each station. To estimate the potential impact of vertical variations in temperature on the C. finmarchicus is subject to predation from a mean stage duration, we computed spatial maps of variety of animals, including chaetognaths, cteno- the vertically averaged stage duration based on the phores, omnivorous copepods, and fish (e.g., Davis, three-dimensional climatological temperature and 1984; Sullivan and Meise, 1996; Dalpadado et al., compared them with stage durations based on the 2000; Sell et al., 2001). The range of mortalities vertically averaged temperature. Ratios of the two inferred herein (0.01–0.2 d 1) generally falls within quantities on GB indicate minor differences, with the envelope of observational estimates of preda- 6 (footnote continued) tion. Interestingly, some of the highest inferred available at: http://userwww.sfsu.edu/ bioocean/research/ mortalities occur on the crest, where the presence of gbpredation/gbpredation1.html. 7Ohman et al. (2002) report a third peak in mortality between 6Specific rates of predation on C. finmarchicus copepodids the egg and second naupliar stage which is not resolved by the based on observed predator abundance and feeding rates are present study because the youngest stage included herein is N3. ARTICLE IN PRESS 2650 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 the stage durations based on vertically averaged Food limitation increases slightly in May–June, temperature slightly longer than those based on the with the average stage duration being 15% longer three-dimensional climatology (2.471.7%, than the temperature limited rate. Clearly the effect 2.371.3%, and 3.771.6%, for January–February, of food is significant, and the mean increase in stage March–April, and May–June, respectively). Thus duration (27%) translates into commensurately the nonlinear relationship between stage duration lower estimates of mortality. Thus food limitation and temperature gives rise to a potential bias, in is a plausible explanation of the systematic differ- that the decrease in stage duration in warmer ences between the present estimates of mortality and surface waters overshadows the increased stage those of Ohman et al. (2002). Indeed, Ohman et al. duration in cooler waters at depth. The longer stage discuss the potential impact of food limitation, duration predicted by the vertically averaged model noting that including this effect could potentially translates linearly into decreased mortality estimates reduce their mortality estimates for feeding stages (Eqs. (1) and (2)). However, the 2–4% increases in (N3 to adult) by up to a factor of two. mortality that would result from more realistic treatment of temperature variability would be 4.3. What causes the absence of late-stage barely perceptible in Fig. 11. Therefore, it does copepodids on the crest in June? not appear that temperature effects on stage duration are sufficient to explain the differences The most salient characteristic of the late spring/ between our mortality estimates and those of early summer decline in copepodids is the near Ohman et al. (2002). Nevertheless, this possibility absence of older stages on the crest (Fig. 3). Term cannot be discounted completely because the above balances computed for the crest region inside the comparison assumes uniform vertical distribution of 60 m isobath indicate that this is primarily a result the animal. Covariance of fluctuations in animal of mortality, although the negative net molting abundance and temperature could introduce addi- fluxes in C3 and C4 also contribute to the decline of tional bias. those stages (Table 2). Advective and diffusive terms A potentially more important difference between are 1–2 orders of magnitude smaller. The modest the two studies is the inclusion of food limitation. influence of the transport terms is also consistent Evaluation of the ratio between stage durations with seasonal modulation of hydrodynamic ex- based on temperature alone (Eq. (3)) with that change between the crest and surrounding waters derived from the combined effects of temperature (Hannah et al., 1998; McGillicuddy et al., 1998). and food (Eq. (5)) permits quantification of this Specifically, development of stratification in the effect (Table 1). Food limitation is significant in summer accelerates an around-bank jet that tends to January–February, with stage durations on GB isolate the crest from upstream supply of animals. 55% longer than they would be based on tempera- This apparent mortality of copepodids on the ture alone. This finding is consistent with the crest is likely due to predation (see above), but there somewhat lower RNA:DNA ratios observed in C. are other factors that could be important. C. finmarchicus in January, which is indicative of food finmarchicus is a boreal animal that prefers colder limitation (Wagner, 2000). The March–April phy- temperatures. Seasonal input of heat into the well- toplankton bloom relaxes this effect, with the food- mixed waters of the crest could make that environ- limited stage durations only 12% longer on average. ment unsuitable, whereas stratified waters of the
Table 1 Mean and standard deviation of the percentage increase in stage duration predicted by a temperature- and food-dependent model over that based on temperature alone
Time period Stage
N4 (%) N5 (%) N6 (%) C1 (%) C2 (%) C3 (%) C4 (%) C5 (%) C6 (%)
January–February 57724 54723 52723 58724 55723 59724 57724 53723 51723 March–April 14717 11717 9717 14717 12717 15717 13717 11717 9717 May–June 17712 14711 13711 17712 15711 18712 16711 14711 12711
Only nodes on Georges Bank included in the computations. ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2651
Table 2
Space-time averaged values of the biological and physical controls of C2–C5 on the crest between May and June
Stage Term
Molting Fi 1 Fi Mortality miCi Advection r ðvCiÞ Diffusion r ðHKrCiÞ=H Tendency qCi=qt
C2 0.9661 2.2759 0.1227 0.0769 1.2640 C3 1.4326 1.1062 0.1061 0.0804 2.5131 C4 2.2027 1.8964 0.0072 0.1429 4.2348 C5 3.0676 5.1040 0.0739 0.1368 2.0993 C6 6.1338 6.3514 0.1780 0.0883 0.4839
Units are # m 3 d 1. bank periphery remain more hospitable because cies in the circulation model to lead to anomalous cooler waters are accessible at depth. Satellite biological inference. However, the most salient imagery indicates sea surface temperatures on the characteristics of the solutions presented herein are crest reach 10–12 1C in late spring/early summer associated with robust features of the circulation on (Bisagni et al., 2001). However, these temperatures GB that are well documented in the literature do not cause deleterious effects on C. finmarchicus (Naimie, 1996; Naimie et al., 2001). Nevertheless, reared in the laboratory (Campbell et al., 2001). the potential for nonlinear impacts of time-depen- Nevertheless, it is possible that more subtle effects dent flows (such as storm events) on the mean of increasing temperatures might adversely affect behavior of the system remains to be investigated. natural populations on the crest, since this is close In this context, it would be beneficial to investigate to the observed upper limit for field populations of the sensitivity of the results to the details of the C. finmarchicus in other parts of its range (Bonnet hydrodynamic fields by performing biological in- et al., 2005). versions on ensembles of perturbations to the climatology that are all equally valid with respect 4.4. Caveats to observations. This is not to say that the vertically averaged There are a number of caveats that must be model used herein is completely sufficient, especially considered in the interpretation of these results. To in stratified conditions. Moreover, C. finmarchicus is begin with, it is not possible to demonstrate a priori capable of controlling its vertical position in the that the assimilation procedure results in a global water column by swimming, and that behavior is minimum of the cost function. The existence of local not included in the present model. Indeed, earlier minima can be investigated by starting from studies have illustrated the potential for layered different initial guesses of the control variables, as organism distributions and vertical shear to have well as restarting the iterative procedure with significant impact on the supply and retention of C. perturbations to the control variables. Both of these finmarchicus on GB. For example, the model of approaches were pursued, and convergence to the Lynch et al. (1998) showed how transport reported solution appears to be stable. That the of copepodids from the deep basins of the Gulf of resulting solution closely resembles the observations Maine to GB is favored by upward swimming (cf. Figs. 3–5) further attests to satisfactory solution of copepodids into the surface Ekman layer, where of the minimization problem. wind-driven surface currents provide a more direct Several aspects of the basic formulation of the transport pathway than the more circuitous flows at inverse problem are also worthy of note. First of all, depth. The fact that this structure is not fully the physical transport fields are specified with represented in the present model would tend to certainty. If the observed changes in abundance diminish the importance of advective supply of C. are incompatible with the prescribed circulation, the finmarchicus to the bank, and is therefore an inversion technique will adjust the control variables important caveat in the present assessment of its (off-bank initial conditions, sources/sinks of N3, importance relative to local biological processes. On and mortality fields) to make up for those dis- the other hand, surface-intensified transport could crepancies. In this sense, it is possible for deficien- also play a role in the export of C. finmarchicus off ARTICLE IN PRESS 2652 X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 the bank. If so, then the vertically averaged model January–June dynamics of C. finmarchicus on GB. could be too retentive, reducing the need for local That the inversion for initial conditions reached sources to maintain the population. It remains to be upstream and deposited animals in the deep basins seen whether vertical structure has more impact on of the Gulf of Maine implies connectivity between supply or removal processes, and the degree to these regions on seasonal time scales. However, the which these might compensate for each other in a sensitivity experiment in which upstream sources vertically averaged model. Clearly, the inclusion of were set to zero showed that the model could still fit vertical dimension is an important avenue for future the data with only modest reductions in the inferred study. mortality and a minor increase in the local source of N3. Thus, advective delivery of animals from 5. Conclusions upstream does not appear to be a major contributor to the vernal population increase in this model. In The fundamental question posed in an inverse other words, the initial conditions prescribed in modeling approach is whether or not a set of data fit January provide a sufficient seed population. Of a particular model. In the present case, the answer is course, the initial conditions themselves were yes. Observations of the climatological distribution influenced to some degree by upstream sources. of C. finmarchicus were assimilated into a physi- Clearly the broader question of self-sustenance of C. cal–biological model based on the climatological finmarchicus on GB begs for a study of the entire circulation. The population dynamics model speci- annual cycle. Observations from the MARMAP fied temperature- and food-dependent stage dura- (Sherman et al., 1996) and ECOMON (Link et al., tion, and the control parameters were off-bank 2002) programs would be quite useful for such initial conditions, a source term for the youngest purposes. In any case, the present results indicate stage in the model (N3), and a seasonally varying the GLOBEC broad-scale surveys resolve a clear stage-specific mortality field. This model fits the signal in the mean seasonal cycle of C. finmarchicus data insofar as the resulting inverse solutions population dynamics that is not severely compro- capture the essential features of the observed mised by advective influences. distributions with values of the control parameters An important next step is to investigate inter- that are not unrealistic. annual variability. Combination of climatological A more stringent test of the model would be physics with climatological biology has illuminated provided by direct measurements of the control some of the controls on the January–June monthly parameters. In principle it would be possible to mean distribution of C. finmarchicus for 1995–1999. alleviate the need to invert for off-bank initial However, both the physical environment and the conditions and sources of N3 by expanding the distribution of C. finmarchicus are prone to sig- geographic coverage of the measurements and nificant departures from climatology (Mountain sampling the distributions of eggs and the first two and Taylor, 1998; Sherman et al., 1998; Greene naupliar stages. Such observations would permit a and Pershing, 2000; Conversi et al., 2001; Durbin more complete model of the life cycle, spanning egg and Casas, 2006). There are several opportunities to through adult stages and including reproduction. explore interannual variability in this context. For However, the issue of mortality remains much more example, the present results could be compared to problematic. C. finmarchicus is subject to predation an analogous inversion of the MARMAP years by a wide variety of organisms, each with their own (1977–1987) to investigate changes in the mean state unique distribution, abundance, and feeding char- of the system between these two epochs. Another acteristics. Observational specification of space– promising avenue would be to compare physical– time fluctuations in the aggregate impact of all biological hindcasts of specific years based on predators on the target species is clearly not detailed three-dimensional hydrodynamic simula- practical. Perhaps the most tractable way forward tions being constructed for the GLOBEC era (Chen is to undertake comprehensive predation studies in et al., 2003). Lastly, the significance of basin-scale a few key locations, and then invert for spatial processes in governing both the mean state and variations in the rates that are constrained by such interannual variability in this region remains to be process studies. investigated. Basin-scale models of C. finmarchicus Diagnosis of the inverse solutions provides some population dynamics are emerging (Speirs et al., insight into the mechanisms controlling the mean 2005), and physical–biological interactions at these ARTICLE IN PRESS X. Li et al. / Deep-Sea Research II 53 (2006) 2632–2655 2653 large scales (e.g., Heath et al., 2004) are a key topic the copepod Calanus finmarchicus reared in the laboratory. for further research. Marine Ecology Progress Series 221, 161–183. Carlotti, F., 1996. A realistic physical–biological model for Calanus finmarchicus in the North Atlantic: a conceptual Acknowledgments approach. Ophelia 44, 47–58. Chen, C.H., Liu, Beardsley, R.C., 2003. An unstructured, finite- This work was supported by the US GLOBEC volume, three-dimensional, primitive equation ocean model: Georges Bank program: Integration and Synthesis application to coastal ocean and estuaries. Journal of Atmo- spheric and Oceanic Technology 20, 159–186. of Georges Bank Broad-Scale Survey Results, Conversi, A., Piontkovski, S., Hameed, S., 2001. Seasonal and sponsored by NSF (OCE-0233800) and NOAA interannual dynamics of Calanus finmarchicus in the (NA17RJ1223). We are grateful for two anonymous Gulf of Maine (Northeastern US shelf) with reference to the reviews that led to substantial improvement over the North Atlantic Oscillation. Deep-Sea Research II 48, original manuscript. We thank Maria Casas for 519–530. providing us access to the zooplankton database. Dalpadado, P., Ellertsen, B., Melle, W., Dommasnes, A., 2000. 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